Electromagnetic gradiometers

ABSTRACT

An electromagnetic gradiometer that includes multiple torsionally operated MEMS-based magnetic and/or electric field sensors with control electronics configured to provide magnetic and/or electric field gradient measurements. In one example a magnetic gradiometer includes a first torsionally operated MEMS magnetic sensor having a capacitive read-out configured to provide a first measurement of a received magnetic field, a second torsionally operated MEMS magnetic sensor coupled to the first torsionally operated MEMS magnetic sensor and having the capacitive read-out configured to provide a second measurement of the received magnetic field, and control electronics coupled to the first and second torsionally operated MEMS magnetic sensors and configured to determine a magnetic field gradient of the received magnetic field based the first and second measurements from the first and second torsionally operated MEMS electromagnetic sensors.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(e) ofco-pending U.S. Provisional Application No. 62/568,627 titled “MAGNETICGRADIOMETERS AND METHODS” and filed on Oct. 5, 2017, which is hereinincorporated by reference in its entirety for all purposes.

BACKGROUND

Precision magnetometers have existed for nearly a century. During theSecond World War, flux-gate magnetometers were applied to detectsubmerged submarines based on the ferromagnetic properties of theirhulls. Since the first use of magnetometers, technology has continued toadvance to enable near-field, quasi-static, magnetometry in theextremely low frequency (ELF) band. Applications of this technologyinclude proximity detection (e.g., ships, submarines, mines, etc.),energy resource prospecting, non-destructive testing of structures(e.g., civil infrastructure, welding joints, etc.), various biomedicalapplications (e.g., magneto-encephalography), communication throughconductive media, and precision current sensing among otherapplications.

However, several important factors have made extending the magnetometertechnology challenging. One of the most recognizable issues is thepresence of significant background interferers. Background interferersquickly mask tiny signal emissions as the range between the source andthe detector is increased. Background interference, often called“clutter”, may be of both natural (e.g., solar activity, such as,lightning) and anthropogenic (e.g., power lines, machinery, etc.)origin. Heavy magnetic shielding can reduce these clutter noise sourcesfor some applications (e.g., biomedical applications). However, magneticshielding is typically extremely expensive, and challenging to extend tofree-field detection scenarios, such as searching for submarines.

Moreover, at very low frequencies, vibrations of the magnetometersensors may produce interference signals as a result of the largerstatic magnetic field of the Earth. Linear motion through the Earth’sgradient is a factor, but for vector magnetometers, the greatestchallenge is the rotational vibration (e.g., jitter), which may causethe very large background field of the Earth to be modulated into thesense bandwidth of the magnetometer. This is especially problematic onmoving platforms. A scalar magnetometer may avoid the first order errorby reducing the total number of degrees of freedom measured; however,scalar magnetometers are limited in the information that they canprovide.

The noise floor of modem magnetometers has been reduced to a level wherethe above-discussed factors dominate the performance of any deployedsystem. For instance, near 1 Hz, the clutter background is often ordersof magnitude (40 - 60 dB) larger than existing precision instruments.Likewise, the resulting jitter induced noise can be much worse andrequire high precision (< 1 nrad/√Hz) instruments for compensation.These instruments are often expensive and may not be available for someapplications.

SUMMARY OF THE INVENTION

Aspects and embodiments are directed to micro-electromechanical systems(MEMS) based sensor systems, including MEMS-based torsionalgradiometers, gradiometer systems, and related methods. In certainexample, multiple low-noise MEMS electromagnetic sensors are coupledtogether to form an electromagnetic gradiometer. The integrated MEMSelectromagnetic sensors may be used to measure some or all components ofa magnetic and/or electric field gradient matrix and vector field.

According to one embodiment, a magnetic gradiometer comprises a firsttorsionally operated MEMS magnetic sensor having a capacitive read-outconfigured to provide a first measurement of a received magnetic field,a second torsionally operated MEMS magnetic sensor coupled to the firsttorsionally operated MEMS magnetic sensor and having the capacitiveread-out configured to provide a second measurement of the receivedmagnetic field, and control electronics coupled to the first and secondtorsionally operated MEMS magnetic sensors and configured to determine amagnetic field gradient of the received magnetic field based the firstand second measurements from the first and second torsionally operatedMEMS electromagnetic sensors.

In one example each of the first and second torsionally operated MEMSmagnetic sensors includes a proof-mass, a magnetic dipole source coupledto the proof mass, and a substrate having a substrate offset spacedefined therein, wherein the proof-mass is suspended above the substrateoffset space, and a first sense electrode disposed on the substratewithin the substrate offset space and positioned proximate theproof-mass, the first sense electrode being configured to measure achange in capacitance relative to the proof mass from torsional movementof the proof-mass in response to the received magnetic field at themagnetic dipole source. In one example each of the first and secondtorsionally operated MEMS magnetic sensors further includes acounterbalance coupled to the proof-mass, wherein the magnetic dipolesource is coupled to a first surface of the proof-mass and thecounterbalance is coupled to a second surface of the proof-mass distalthe magnetic dipole source. In another example each of the first andsecond torsionally operated MEMS magnetic sensors further includes asecond sense electrode disposed on the substrate, and wherein the firstsense electrode and the second sense electrode are configured to providea differential capacitance measurement based on the change incapacitance from the torsional movement of the proof-mass. Each of thefirst and second torsionally operated MEMS magnetic sensors may furtherinclude at least one drive electrode positioned proximate the proof-massand configured to produce a feedback torque on the proof-mass. In oneexample the magnetic dipole source is a permanent magnet. In one examplethe permanent magnet is a Neodymium Iron Boron (NdFeB) rare Earthpermanent magnet. In another example each of the first and secondtorsionally operated MEMS magnetic sensors further includes at least onesupport coupled to the proof-mass and configured to suspend theproof-mass above the substrate offset space. The magnetic fieldgradiometer may further comprise an electronic feedback loop configuredto stabilize a scale factor of the magnetic field gradiometer bymonitoring and adjusting a resonant frequency of the at least onesupport.

In one example the magnetic gradiometer further comprises a circuitboard that electrically couples the first torsionally operated MEMSmagnetic sensor to the second torsionally operated MEMS magnetic sensor,wherein the control electronics is formed on the circuit board. Themagnetic gradiometer may further comprise a reference structure thatmagnetically couples the first torsionally operated MEMS magnetic sensorto the second torsionally operated MEMS magnetic sensor. In one examplethe magnetic gradiometer further comprises at least one reference magnetthat produces a reference magnetic field configured to mutually alignthe first and second torsionally operated MEMS magnetic sensors to acommon vector such that their magnetic moments are aligned. In anotherexample the magnetic gradiometer further comprises a high permeabilityshunt that couples together the first and second torsionally operatedMEMS magnetic sensors and the at least one reference magnet. In oneexample the high permeability shunt includes a soft ferrite cageconfigured to provide shielding for the control electronics.

According to another embodiment an electric field gradiometer comprisesa first torsionally operated MEMS electric field sensor having acapacitive read-out configured to provide a first measurement of areceived electric field, a second torsionally operated MEMS electricfield sensor coupled to the first torsionally operated MEMS electricfield sensor and having the capacitive read-out configured to provide asecond measurement of the received electric field, and controlelectronics coupled to the first and second torsionally operated MEMSelectric field sensors and configured to determine an electric fieldgradient of the received electric field based the first and secondmeasurements from the first and second torsionally operated MEMSelectric field sensors.

In one example the electric field gradiometer further comprises at leastone electric field generator that produces a reference field configuredto mutually align the first and second torsionally operated MEMSelectric field sensors to a common vector such that their electricdipole moments are aligned.

According to another embodiment an integrated electromagneticgradiometer array comprises at least two magnetic gradiometers, eachmagnetic gradiometer including a first torsionally operated MEMSmagnetic sensor having a magnetic field capacitive read-out configuredto provide a first measurement of a received magnetic field, a secondtorsionally operated MEMS magnetic sensor coupled to the firsttorsionally operated MEMS magnetic sensor and having the magnetic fieldcapacitive read-out configured to provide a second measurement of thereceived magnetic field, and magnetic sensor control electronics coupledto the first and second torsionally operated MEMS magnetic sensors andconfigured to determine a magnetic field gradient of the receivedmagnetic field based the first and second measurements from the firstand second torsionally operated MEMS electromagnetic sensors.

In one example the integrated electromagnetic gradiometer array furthercomprises at least one electric field gradiometer, the at least oneelectric field gradiometer including a first torsionally operated MEMSelectric field sensor having an electric field capacitive read-outconfigured to provide a first measurement of a received electric field,a second torsionally operated MEMS electric field sensor coupled to thefirst torsionally operated MEMS electric field sensor and having theelectric field capacitive read-out configured to provide a secondmeasurement of the received electric field, and electric field sensorcontrol electronics coupled to the first and second torsionally operatedMEMS electric field sensors and configured to determine an electricfield gradient of the received electric field based the first and secondmeasurements from the first and second torsionally operated MEMSelectric field sensors.

In another example the integrated electromagnetic gradiometer arrayfurther comprises at least one torsionally operated MEMS electric fieldsensor having an electric field capacitive read-out configured toprovide measurements of a received electric field. In another examplethe integrated electromagnetic gradiometer array further comprises atleast one additional torsionally operated MEMS magnetic sensor havingthe magnetic field capacitive read-out configured to provide acorresponding at least one additional measurement of the receivedmagnetic field.

Still other aspects, embodiments, and advantages of these exemplaryaspects and embodiments are discussed in detail below. Embodimentsdisclosed herein may be combined with other embodiments in any mannerconsistent with at least one of the principles disclosed herein, andreferences to “an embodiment,” “some embodiments,” “an alternateembodiment,” “various embodiments,” “one embodiment” or the like are notnecessarily mutually exclusive and are intended to indicate that aparticular feature, structure, or characteristic described may beincluded in at least one embodiment. The appearances of such termsherein are not necessarily all referring to the same embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects of at least one embodiment are discussed below withreference to the accompanying figures, which are not intended to bedrawn to scale. The figures are included to provide illustration and afurther understanding of the various aspects and embodiments, and areincorporated in and constitute a part of this specification, but are notintended as a definition of the limits of the invention. In the figures,each identical or nearly identical component that is illustrated invarious figures is represented by a like numeral. For purposes ofclarity, not every component may be labeled in every figure. In thefigures:

FIG. 1 is a diagram of one example of a magnetic sensor incorporating afrequency-based torque measurement mechanism according to aspects of thepresent invention;

FIG. 2 is a diagram showing a partial exploded view of one example of apackaged magnetic sensor according to aspects of the present invention;

FIG. 3A is a diagram showing a partial exploded perspective view of oneexample of an electric field sensor according to aspects of the presentinvention;

FIG. 3B is a diagram showing another perspective view of the electricfield sensor of FIG. 3A;

FIG. 4 is a diagram showing a perspective view of one example of atorsionally operated magnetic sensor having a capacitive read-outaccording to aspects of the present invention;

FIG. 5 is a simplified circuit diagram of one example of controlelectronics for a magnetic sensor and gradiometer according to aspectsof the present invention;

FIG. 6 is a block diagram one of example of magnetic gradiometeraccording to aspects of the present invention;

FIG. 7 is a graph showing simulated measurements of scale factor as afunction of frequency for different bias voltages in a modeled exampleof a magnetic gradiometer according to aspects of the present invention;

FIG. 8A is a graph showing simulated measurements of various sources ofmagnetic noise in a modeled example of a magnetic gradiometer accordingto aspects of the present invention;

FIG. 8B is a graph showing simulated measurements of the total magneticnoise for different bias voltages in the modeled example of a magneticgradiometer according to aspects of the present invention;

FIG. 9 is a graph showing the temperature dependence of themagnetization in a modeled example of a magnetic gradiometer accordingto aspects of the present invention; and

FIG. 10 is a block diagram of one example of a gradiometer array includea pair of magnetic gradiometers according to aspects of the presentinvention.

DETAILED DESCRIPTION

Although magnetics technology may be viewed as mature, advancingapplications continue to drive the need to develop and improve precisionmagnetometers. For example, the advent of low cost unmanned aerialvehicles, has provided an avenue to improve the cost effectiveness oflarge-scale magnetic surveys. This in turn drives a need to achieve veryhigh levels of performance (low noise) while operating in the Earthfield with low size, weight and power (SWaP).

The various challenges associated with magnetometers discussed abovehave prevented the widespread adoption of advanced magnetometer systemsthat operate in the open ambient field of the Earth. One approach toaddressing the discussed challenges includes measuring a magnetic fieldgradient instead of the field itself. The gradient of clutter, whichtends to come from distant sources, is remarkably different than thesignal source, which tends to be at a much closer range to the sensor.Therefore, the gradient provides an orthogonal measurement that allowsthe signal and clutter to be separated from one another. A rigidgradiometer also has the advantage that the first order vibration errorsare also eliminated from the measurements. A gradiometer thereforeoffers a mechanism to eliminate the most problematic system issues oftraditional Earth-field magnetometers. Nonetheless traditionalgradiometers are not without their own drawbacks. In particular,measurements of magnetic field gradient fall off as 1/r⁴ with range (r)from the source dipole of the signal. Accordingly, detection becomesdifficult for many important applications, such as submarine detection.

Aspects and embodiments of the devices and methods disclosed hereinaddress the drawbacks associated with typical magnetometers andgradiometers, while also improving performance such that signals may bemeasured at great ranges in the ambient Earth field. In particular,certain aspects and embodiments are directed to MEMS based torsionalmagnetometers which are able to address the modern needs of integrationon small mobile platforms. As discussed in more detail below, MEMS-basedsensors can be configured to measure differential torques generated bymagnetized structures exposed to a magnetic field. MEMS-based magneticgradiometers according to certain examples may include transducers thatare coupled magnetically and electrically, with an ability to tune tonear zero stiffness, or operate in a resonant mode, for maximumsensitivity and bias stability. Examples of the MEMS-based magneticgradiometers disclosed herein may simultaneously achieve low-noise(e.g., less than 100 fT/√Hz), high dynamic range (e.g., greater than 50µT) operation in a small volume (e.g., less than 100 cm³) to enableproduction of a high performance airborne magnetometry system havingSWaP compatible with low-cost platforms, such as small unmannedaircraft. Moreover, examples of the magnetic gradiometers disclosedherein may eliminate the need for costly shielding and/or Earth-fieldcompensation associated with conventional ground-based systems. Inaddition, certain aspects and embodiments are directed to MEMS-basedelectric field sensors that use similar torsional sensor technology.Such sensors may open up new opportunities in biophysical sensing, forexample. In particular, non-contact measurement of electric fields fromthe brain offers a mechanism to make widespread cognitive feedbackpractical, and benefit numerous applications, including cognitiveenhancement and optimized training, brain computer interfaces, diagnosisand treatment and treatment of neurological conditions, and mal-intentdetection. In addition, the MEMS-based electric field sensors may beused to take other types of biophysical measurements, such as heart ratemeasurements, for example.

It is to be appreciated that embodiments of the methods, systems, andapparatuses discussed herein are not limited in application to thedetails of construction and the arrangement of components set forth inthe following description or illustrated in the accompanying drawings.The methods, systems, and apparatuses are capable of implementation inother embodiments and of being practiced or of being carried out invarious ways. Examples of specific implementations are provided hereinfor illustrative purposes only and are not intended to be limiting.Examples disclosed herein may be combined with other examples in anymanner consistent with at least one of the principles disclosed herein,and references to “an example,” “some examples,” “an alternate example,”“various examples,” “one example” or the like are not necessarilymutually exclusive and are intended to indicate that a particularfeature, structure, or characteristic described may be included in atleast one example. The appearances of such terms herein are notnecessarily all referring to the same example. Also, the phraseology andterminology used herein is for the purpose of description and should notbe regarded as limiting. The use herein of “including,” “comprising,”“having,” “containing,” “involving,” and variations thereof is meant toencompass the items listed thereafter and equivalents thereof as well asadditional items. References to “or” may be construed as inclusive sothat any terms described using “or” may indicate any of a single, morethan one, and all of the described terms. Any references to front andback, left and right, top and bottom, upper and lower, and vertical andhorizontal are intended for convenience of description, not to limit thepresent systems and methods or their components to any one positional orspatial orientation.

As discussed above, certain embodiments are directed to a magneticgradiometer. In various examples, the magnetic gradiometer includes oneor more MEMS-based magnetic sensors. FIG. 1 is a diagram of one exampleof a MEMS-based torsionally operated magnetic sensor 100 according tocertain embodiments. In the illustrated example, the MEMS-based magneticsensor 100 includes a proof-mass 102 that includes a magnetic dipolesource. The magnetic dipole source may be a hard magnet (e.g., aNeodymium Iron Boron (NdFeB) rare Earth permanent magnet). Theproof-mass 102 is placed on (or otherwise attached to) a Siliconstructure 104. The Silicon structure 104 is attached to a plurality ofsupports 106, 108, 110, 112. In various examples, the plurality ofsupports 106, 108, 110, 112 act like springs, and movement of theproof-mass 102 is constrained by the spring force of each support,damping forces, and inertial forces. The magnetic sensor 100 furtherincludes a plurality of geometric isolation structures 114, 116 whichmay isolate the plurality of supports 106, 108, 110, 112 from adifferential thermal strain between the proof-mass 102 and the pluralityof supports 106, 108, 110, 112. FIG. 1 shows an example of an “H-shaped”arrangement which may reduce the sensitivity of the sensor 100 to errorsby substantially isolating the plurality of supports 106, 108, 110, 112from thermal deformations. In the example of FIG. 1 , a first geometricisolation structure 114 is interposed between a first support 106 andthe proof-mass 102, and a second support 108 and the proof-mass 102.Similarly, a second geometric isolation structure 116 is interposedbetween a third support 110 and the proof-mass 102, and a fourth support112 and the proof-mass 102. Each isolation structure 114, 116 maysuspend the proof-mass 102 relative to a mounting surface, such as ashared substrate 118 (e.g., silicon or glass substrate). The sharedsubstrate 118 may support additional components of the sensor 100, andmay provide routing for electrical contacts 120. Electrical contacts 120may be used to electrically couple various components of the sensor 100to external circuitry or devices.

In the example shown in FIG. 1 , the first geometric isolation structure114 and the second geometric isolation structure 116 suspend theproof-mass 102 in an opening 122 defined by the shared substrate 118.The opening 122 in the substrate 118 may allow access to a backside ofthe proof-mass 102, which may make attaching the magnetic dipole sourceeasier. As illustrated, each geometric isolation structure 114, 116includes a first arm (e.g., fork-shaped arm) coupled to the proof-mass102 and a second arm (e.g., serpentine-shaped arm) coupled to therespective supports. As shown, each of the geometric isolationstructures 114, 116 extend in a direction across the opening that issubstantially parallel to a direction of extension of the respectivesupports. Accordingly, the geometric isolation structures 114, 116position each support 106, 108, 110, 112 in an orientation that issubstantially orthogonal to a direction of thermal expansion of theproof-mass 102. Accordingly, the geometric isolation structures 114, 116geometrically reduce the thermal sensitivity of each of the supports106, 108, 110, 112. In the example shown in FIG. 1 , each of the supportbeams 106, 108, 110, 112 is split into a fork to further reduce dampinglosses.

The hard magnet generates a magnetic dipole which produces a torque onthe proof-mass 102 when exposed to a magnetic field. The torque impartedon the proof-mass 102 generates an axial force on the plurality ofsupports 106, 108, 110, 112. The torque may be determined directly, orindirectly, to determine one or more characteristic of the magneticfield, such as the magnetic field strength. In particular, an externalmagnetic field (B_(external)) will generate a torque (τ) on theproof-mass 102 due to a remnant dipole (m_(m)) of the magnet. The torqueis given by:

τ = m_(m) × B_(external)

The remnant dipole scales linearly with its dimensions (e.g., x, y, andz) and remnant magnetization (B_(r)), as shown by Equation (2):

$m_{m} = x \cdot y \cdot z \cdot \frac{B_{r}}{\mu_{r} \cdot \mu_{0}}$

The resulting torque can be measured in various ways to determine acomponent of the external magnetic field. In certain examples, anoptical read-out can be used to measure the torque. In such examples,the proof-mass 102 can be constrained by a fixed spring on the Siliconstructure 104, and an optical source (e.g., a laser) may direct opticalradiation to and detect reflected radiation from the surface of theproof-mass 102. Deflection of the proof-mass 102 due to the torquecauses deflection of the impinging optical beam and may cause theoptical beam power to be preferentially split between two opticaldetectors. The dynamics of the MEMS resonator may be leveraged toamplify the motion of the proof mass. The different read-outs from thetwo detectors based on the different received optical power levels maybe used to determine the torque, and from the torque, the magnetic fieldstrength can be determined based on Equations (1) and (2) above. In suchexamples the substrate may be formed from transparent glass to permitdisplacement of the proof mass to be measured optically.

In the example shown in FIG. 1 , the sensor 100 includes afrequency-based read out mechanism. In this example, the plurality ofsupports 106, 108, 110, 112 permit displacement of the proof-mass 102.The magnet generates a torque (τ) in response to an external magneticfield (B), and in response to the torque, the supports 106, 108, 110,112 go into tension and compression due to the imposed forces. Theresonant frequency of each support beam changes with the imposed force,and therefore may be measured to determine the component of the receivedmagnetic field.

In various embodiments, a MEMS comb drive 124 may be used to interfaceand measure the frequency of each support 106, 108, 110, 112 and therebydetermine the imposed forces and resulting external field. The MEMS combdrive 124 may include electrostatic comb fingers and associatedelectronics. In certain examples, each comb drive 124 include a motorcomponent and a sense component positioned on either side of the comb ofthe corresponding support 106, 108, 110, 112. A voltage applied by themotor component causes the motor component, comb, and sense component tobe drawn together. The resonant frequency of each support 106, 108, 110,112 is proportional to the force. Accordingly, respective comb drivecapacitances may be used to measure the resonant frequency of thecorresponding support 106, 108, 110, 112. Signals from the electronicsof the MEMS comb drives 124 may be provided to external components ordevices via the electrical contacts 120. Multiple independent supports106, 108, 110, 112 and frequency measurements also enable two axes ofacceleration and a common mode signal (temperature) to be measured withhigh precision. Frequency can be measured over a very large dynamicrange, and provides the ability to resolve fT/√Hz signals from a smalldevice in the presence of a large variable field typical of a sensorbeing placed on a maneuvering vehicle. Further examples and discussionof a frequency-based read-out approach for a MEMS-based magnetic sensorare described in U.S. PG-Pub. No. 2017/0097394 published on Apr. 6,2017, which is herein incorporated by reference in its entirety for allpurposes.

A capacitive read-out mechanism may also be used. For example, one morecapacitive plates may be used to capacitively sense movement of theproof-mass 102 and determine the torque. Examples and discussion of acapacitive read-out approach for a MEMS-based magnetic sensor aredescribed in U.S. Pat. Application No. 15/944,234 titled “MINIATUREMAGNETIC FIELD DETECTOR” and filed on Apr. 3, 2018, which is hereinincorporated by reference in its entirety for all purposes.

Referring to FIG. 2 , the magnetic sensor 100 may be packed within ahousing to reduce the presence of conductive materials near the sensor.In certain examples, the housing may facilitate a vacuum environment orcryogenic environment to further reduce damping effects within thesensor 100. In the example shown in FIG. 2 , the housing includes aceramic baseplate 126, and intermediate mounting surface 128, and a lidsubstrate 130. The lid substrate 130 may be made of Alumina or glass,for example. The shared substrate 118 may be attached to the ceramicbase plate 126, as shown in FIG. 2 . An internal shield 132 may extendfrom the ceramic base plate 126 to shield portions of the sharedsubstrate 118 and reduce noise interference from electronic componentsof the sensor 100. In certain examples, the internal shield 132 may becomposed of a non-conductive material with a high magnetic permeability.A MEMS process for a counterbalance (or countersink) may also be used toreduce mass imbalance which would introduce pendulous errors fromvibration. As illustrated, in certain embodiments the packaged sensor100 may include one or more field concentrators 134 positioned andarranged to focus the magnetic field on the proof-mass 102. For example,the field concentrators 134 may include various flux concentrators, suchas soft magnetic materials. The field concentrators 134 may bepositioned on the intermediate mounting surface 128 which is configuredto rest on a top surface of the internal shielding 132. When coupledwith the internal shielding 132, an opening 136 defined in theintermediate mounting surface 128 rests substantially proximate theproof-mass 102 so as to permit the receipt of magnetic radiation at aproof-mass 102.

As discussed above, various embodiments provide an electric fieldsensor. Embodiments of the electric field sensor may be constructedsimilar to the magnetic sensor discussed above, and may use a capacitiveread-out to measure rotation of the proof mass. FIGS. 3A and 3Billustrate perspective views of an electric field detector 200 accordingto various examples described herein. FIG. 3A illustrates a view of thedetector 200 with a housing 210 detached from the detector 200, and FIG.3B shows a view of the detector 200 with the housing 210 attached. Thehousing 210 may be removed in a vertical direction away from thedetector 200 (e.g., direction 224), as shown in FIG. 3A. The housing 210may be made of Alumina or glass, for example.

In the example of FIGS. 3A and 3B, the electric field detector 200includes a MEMS-based resonator, which may be defined by processing astructure wafer (e.g., a Silicon-on-Insulator wafer) to a desiredgeometry. As shown, the detector 200 may include a proof-mass 202coupled to a source of concentrated charge 204, a plurality of supports206 a, 206 b (collectively “supports 206"), one or more fluxconcentrators 208 a, 208 b (collectively “flux concentrators 208"), thehousing 210, one or more anchors 212 a, 212 b (collectively “anchors212”), a baseplate 214, one or more electrical contacts 216, one or moreleads 218, and a substrate 222, among other components. While not shownin FIGS. 3A and 3B, each of the contacts 216 may couple the electricfield detector 200 to a control circuit or other external circuitry ordevices. In certain examples, the structure wafer is processed (e.g.,etched) to define the proof-mass 202, the plurality of supports 206, andthe one or more anchors 212. In further examples, the electric fielddetector 200 may also include one or more counterbalances 226 that arecoupled to the proof-mass 202. As discussed above, the counterbalances,which may also be used in the magnetic sensor 100, may be used to reducemass imbalance which would introduce pendulous errors from vibration.The flux concentrators 208 may reduce the effective noise floor.

In certain examples, the electric field detector 200 may also includeone or more sense electrodes and one or more drive electrodes, each ofwhich are positioned on the substrate 222 and obscured in FIGS. 3A and3B by the counterbalance 226. As shown, the substrate 222 is positionedon the baseplate 214. The structure of the electric field detector 200is similar in many ways to that of the magnetic sensor 100 discussedabove, with the magnet replaced by the source of concentrated charge204. In various examples, the source of concentrated charge 204 mayinclude any suitable source of a semi-permanent static electric dipole,such as an electret or a capacitor plate having a residual free chargeand/or polarization. As will be understood to one of ordinary skill inthe art, the term “electret” refers to the electrical analog of apermanent magnet. The electret quasi-permanently traps large charge nearthe breakdown limit of the dielectric material. Examples of suitableelectret materials include, but are not limited to,Polytetrafluoroethylene (PTFE), silicon nitride, Fluorinated EthylenePropylene (FEP), a Perfluoroalkoxy alkane (PFA) material, Cyptop,Cylotene, and other dielectrics. In certain examples the electret mayinclude, but is not limited to, Thermo-electrets, MPEs (metal-polymerelectrets), Radio-electrets, and Mechanoelectrets.

In various examples, the electric field detector 200 determines one ormore characteristics of a received electric field, which one instance isa bio-electrical signal, based on measured capacitance variations due totorsional motion of the proof-mass 202 in response to receiving theelectric field. While in some examples, a combination of linear forcesmay result in the torsional motion of the proof-mass 202, in certainother examples, a variation in capacitance as a result of a singlelinear force may be measured. The proof-mass 202 is supported by theplurality of supports 206, each of which form a rotationally compliantspring anchored to the substrate 222 via a respective anchor 212 a, 212b. In the shown example, each support 206 is a flexured beam interposedbetween a side surface of the proof-mass 202 and a corresponding anchor212 a, 212 b.

Still referring to FIGS. 3A and 3B, in various examples, the pluralityof supports 206 may suspend the proof-mass 202 above a substrate offsetspace defined in the substrate 222. That is, the substrate 222 mayinclude an area (referred to as a “substrate offset space”) formed in asurface thereof beneath the proof-mass 202 (e.g., and counterbalance 226shown in FIGS. 2A and 2B). The substrate offset space is obscured inFIGS. 3A and 3B by the counterbalance 226. While described as beingsuspended “above” the substrate offset space, in other examples, theproof mass 222 may be partially positioned within the substrate offsetspace. In other examples, the proof mass 202 may be positioned in closeproximity to the substrate offset space but not directly above thesubstrate offset space. As discussed above, in certain examples, theelectric field detector 200 may include one or more sense electrodes andone or more drive electrodes, each of which are positioned on thesubstrate 222 and in capacitive communication with the proof-mass 202.

In various examples an impinging electric field concentrated on thesource of concentrated charge 204 generates a torque and effects motionof the proof-mass 202. For instance, the torque, τ, may be representedas:

τ = p × E

where, p, is the strength of the electric dipole from the source ofconcentrated charge 204 (e.g., in C-m) and, E, is the strength of thereceived electric field (e.g., in V/m).

In many instances, the proof-mass 202 responds to the torque by rotatingabout a torque axis (shown as axis τ in FIGS. 2A and 2B). In oneexample, the rotation can be represented as:

$\theta = \frac{\tau}{(\text{Is}^{2}) + (\text{Ds}) + \text{k}}$

where, θ, is the angle of rotation, τ, is the torque, I, is the polarmoment of inertia, s, is the complex frequency, D, is a dampingcoefficient, and k is the rotational stiffness. In this way, the torquegenerated from the electric field induces motion in the proof mass 202,which reacts against the stiffness of the supports 206.

Embodiments of the electric field detector 200 include a capacitiveread-out that is used to measure the torque induced by the electretcoupled to the proof-mass 202. In various examples, the rotation of theproof-mass 202 increases or decreases the distance between the proofmass 202 and the sense electrode(s) positioned on the substrate 222. Asthe distance between the proof mass 202 and the sense electrode(s)increases or decreases, the relative capacitance between the senseelectrode(s) and the proof mass 202 varies. The resulting change incapacitance can be measured by the electronics to estimate thecharacteristics of the received electric field.

Further examples and details of embodiments of electric field detectorswith capacitive read-outs are described in U.S. Pat. Application No.15/944,106 titled “MINIATURE ELECTRIC FIELD DETECTOR” and filed on Apr.3, 2018, which is herein incorporated by reference in its entirety.

According to certain embodiments, a gradiometer design starts with thefundamental building block of the torsionally operated electric ormagnetic field sensor coupled to a readout of one or more capacitivesensor plates and/or electronics, similar to those discussed above withreference to the electric field detector 200. FIG. 4 is a diagramshowing a perspective view of one example of a torsionally operatedmagnetic sensor incorporating a capacitive read-out according to certainembodiments. In this example, the magnetic sensor 300 includes theproof-mass 102 including a hard magnet, such as a Neodymium Iron Boron(NdFeB) magnet, placed on (or otherwise coupled to) a MEMS structure302, which optionally includes a counterweight as discussed above. Theproof-mass 102 rotates and generates a differential capacitance changewhich is measured by the electronics. Operation of the capacitiveread-out is essentially the same as described above with reference tothe electric field sensor 200, only the variations in capacitanceprovide magnetic field measurements rather than electric fieldmeasurements. The electronics provide force feedback via a set ofelectrodes positioned under the proof-mass 102 (and therefore not shownin FIG. 4 ) to rebalance the sensor against any external forces andtorques. Electrical traces 304 for the capacitive sensor plates and/orelectronics may be wire bonded to the ceramic baseplate 126 and coupledto through vias 306 to route electrical signals outside of the sensorpackage. The lid substrate 130, which may be a glass lid, may be bondedto the baseplate 126, optionally including a braze seal 308, to providea vacuum environment which minimizes gas damping of the proof-mass 102as discussed above. The structural supports (e.g., beams or springs) ofthe magnetic sensor 300 can be arranged, as discussed above, such thatthe proof-mass 102 is free to rotate about two axes such that it canmeasure the two vector components which are orthogonal to themagnetization direction of the magnet included in the proof-mass 102. Toaccommodate such an embodiment, the electrodes may be split.

FIG. 5 is a block diagram of one example of the electronics for themagnetic sensor 300. In various examples, the electronics (e.g.,electrical readout circuity) measures the differential capacitance dueto changes in a gap between the Silicon structure 104 and the electrodeslocated on the substrate 116 below the proof-mass 102 (e.g., 3-5 micronsbelow the proof mass). The electronics includes a precision carriergenerator 310 that generates a low noise carrier signal. The low noisecarrier signal and bias are applied to torsional magnetic transducers312, which include the proof-mass 102 and MEMS structure 302, toup-convert the measured signal and avoid 1/f noise sources in theelectronics. The measured signal from the magnetic transducers 312 isamplified, for example, by a pre-amplifier 314 and a low-noiseAC-coupled instrumentation amplifier 316, and demodulated (representedat block 318) to recover the original (torque) signal. Filters,including filters 320 and optionally other filters not shown in FIG. 5 ,may be employed throughout the electronics to minimize out-of-bandnoise. Various additional amplifiers, including amplifiers 322 andoptionally other amplifiers not shown in FIG. 5 , may be employedthroughout the electronics to adjust the power levels of the varioussignals, as will be appreciated and understood by those skilled in theart, given the benefit of this disclosure. After amplification andfiltering, digital electronics can be employed for a variety ofpost-processing tasks and ultimate use. A loop controller 324 may beincluded and configured to adjust the bias and/or provide controlsignals to the transducers 312 and optionally other components of theelectronics and magnetic sensor 300. In some examples, differentialcapacitors (A and B in FIG. 5 ) may be integrated on a single die.However, in other examples, differential measurements between multipletransducers 312 that are on separate dies may be used. Despite not beingco-located, the transducers may be force coupled and operate as a singleinstrument.

FIG. 6 is a diagram of one example of a magnetic gradiometer 400configured to measure two B-field components and two gradients,according to certain embodiments. As discussed in more detail below, theintegrated system provides electrical and magnetic coupling between twotransducers 300 a, 300 b, along with force feedback, to generatelow-noise magnetic field measurements over a wide dynamic range.According to certain examples, the magnetic gradiometer 400 isconfigured to difference the output from the two transducers 300 a, 300b to obtain the gradient measurements. Scale factor variations from onetransducer to the other may be addressed by electrically andmagnetically coupling the two transducers 300 a, 300 b together, suchthat they can operate as an integrated gradiometer.

Referring to FIG. 6 , in this embodiment, the magnetic gradiometer 400includes the two magnetic transducers 300 a, 300 b, each of which may bean embodiment of the torsionally operated magnetic sensor 300 discussedabove. Each transducer 300 a, 300 b can be configured to makedifferential capacitance measurements between capacitive plates disposedon opposite sides of the proof-mass 102 such that one capacitanceincreases and the other decreases due to rotation of the proof-mass 102,as discussed above. According to certain examples, the capacitivedifference approach may be extended by taking capacitance measurementsthat are differenced between two transducers placed a distance apart.Thus, as shown in FIG. 6 , the two transducers 300 a, 300 b may beplaced at opposite ends of the housing structure. A circuit board 402may link the two transducers 300 a, 300 b together, with the desireddata easily extracted. The circuit board 402 may include edge connectors(not shown), and a connector port 404 for coupling the gradiometer 400to external circuitry or devices. Each transducer 300 a, 300 b can bemade to rotate in two axes (orthogonal to the magnetization along thelong z-axis) and will therefore respond to external magnetic fields inthe x- and y-axes. Thus, from Equation (1) above, each transducer 300 a,300 b provides torque measurements:

τ_(x) = m_(z) × B_(y)

τ_(y) = m_(z) × B_(x)

Each transducer 300 a, 300 b can be independently measured and providestwo gradients (dBx/dz and dBy/dz) when differenced along the long (z)axis. Accordingly, two measurements of each gradient can be made, andcan be averaged together to reduce the readout noise by √2 per axis.Variations from one transducer to the other are common mode to firstorder. In order to maximize scale factor stability, and absolutemeasurement accuracy, tunable bias voltages on the electrodes (e.g.,torque plates) allow the scale factor to be measured and stabilized in acontrol loop, for, example, using the loop controller 324.

In various examples, the two transducers 300 a, 300 b are alsomagnetically coupled through a common reference structure. The magnetson each of the respective proof-masses 102, as well as reference magnets406, are coupled along the long axis (z axis in the example illustratedin FIG. 6 ) of the reference structure and linked together through ahigh permeability shunt 408 that spans the remaining distance betweenthe two sides. In one example the high permeability shunt 408 includes asoft ferrite cage that may also provide shielding for the electronics.The reference field from the reference magnets 406 mutually aligns eachtransducer 300 a, 300 b to a common vector such that all of theirmagnetic moments are aligned. The reference magnets 406 may producefields which are a significant fraction of a Tesla in the vicinity ofeach transducer 300 a, 300 b. This acts as a strong magnetic springsince the field from the reference magnets 406 generates a restoringtorque on the magnet of each proof-mass 102. For instance, a referencefield of -0.6 T produces a magnetic spring that yields a resonantfrequency of greater than 1 kHz. This, along with any mechanical springstiffness, works against the negative torque that is generated andenables large bias voltages to be placed on the respective capacitiveplates. The electrostatic spring, generated by the bias voltage, canthen be chosen to tune the natural frequency of each sensor support,with the ability to greatly increase the scale factor of the systemwhile remaining structurally robust. For example, the device stiffnesscan be tuned by tuning the bias voltage under each plate in thetransducers 300 a, 300 b to generate a negative stiffness whichcounteracts the mechanical stiffness of the system. This tunes theresonance and reduces the contribution of electronics noise in theresonance bands. In certain examples, the combined springs can bebrought to near zero stiffness with properly applied voltage andcontrol. However, a 3 dB broadband performance may be limited to a fewhundred Hertz depending upon the specific design. Achieving equivalentnoise at higher frequencies may be accomplished by reducing the biasvoltage and tuning the natural frequency to the desired sense band. Thisallows the device to operate near its theoretical limit across a broadrange of frequencies (> 1 kHz).

A difference in the external torque between the two sensors (transducers300 a, 300 b), due to a magnetic gradient, generates a differentialcapacitance that is exploited to directly measure the gradient. Theinterplay between the magnetic stiffness and electrical stiffness allowsthe sensor resonant frequency to be tuned. This can be employed tooptimize the noise performance of the gradiometer 400 in selected bands,and can also be monitored to directly measure selected error terms. Forinstance, although uniform thermal changes may common mode (e.g.,cancel) between two perfect transducers, thermal gradients and otherimperfections may not. Since the magnetic moment in the torque equationis a function of temperature, thermal gradients may induce scale factorchanges that leak through any differencing operation between sides andimpact the absolute accuracy of the values measured. However minorchanges in the magnetic moment, will also change the magnetic springstiffness and the resonant frequency. This shift in resonant frequencycan be precisely measured and can be used to directly remove scalefactor variations. Therefore, the electrostatic and magnetic couplingserves to remove the most serious errors encountered when operating in agradiometer mode. There is sufficient margin relative to the vacuumfield emission limit (-200 MV/m) to provide a high enough tuning voltageto reduce the effective total stiffness. In addition, operating at lowerstiffness may increase the scale factor and improve overall noiseperformance at lower frequencies. In certain examples, the electronicsmay provide feedback to linearize the output while tuning the naturalfrequency to maximize the scale factor for a given bandwidth.

According to certain examples, although the proof-masses 102 may berebalanced via electrostatic feedback, there may still be some level ofmotion that will generate variable fields nearby. This intrinsically isnot a problem, since the mechanical structures (e.g., supports) and/orelectrostatic force feedback in each transducer 300 a, 300 b can counterthe static fields from the reference magnets 406, which approach afraction of 1 T. However, residual motion from the force feedback loop,or if a sensor is run in an open loop condition, may generate fieldvariations in transducers immediately nearby if a large signal ispresent (e.g., large maneuvers in the Earth field). In various examples,this effect may be eliminated by ensuring the force feedback dynamicsminimize residual motion. However, in other examples, all of the valuesmay be measured and solved for the cross coupling (e.g., inpost-processing) to correct for the cross talk. This may, in essence, bea magnetic amplifier and produce a scenario where the response of thecenter array element would scale as k*N where k is the coupling factor,which may be greater than 1 for closely spaced geometries. Incomparison, the noise on the center element does not change so there isa net gain in the signal-to-noise ratio (SNR) which scales as N.

Embodiments of the gradiometer 400 can be integrated into a compactpackage. For example, embodiments of the gradiometer 400 may have adimension 410 that is on the order of 1 cm.

The performance of the gradiometer 400 was evaluated by modeling majorerror sources and other performance contributors. A one degree offreedom model describing the scale factor (SF; rad/T) dynamics of asingle-sided MEMS device, such as in the gradiometer 400, is:

$SF = \frac{x_{m} \cdot y_{m} \cdot z_{m} \cdot \frac{B_{m}}{\mu_{0}}}{I \cdot s^{2} + D \cdot s + k_{mech} + k_{mag} + k_{\nu bias}}$

In Equation (5), I is the polar moment of inertia of the rotatingstructure, s is the complex frequency, D is the damping due to losses inthe system, kmech is the mechanical stiffness of any flexure supports,kmag is the magnetic spring stiffness, and kVbias is the springstiffness of the electrostatic spring due to the applied voltage betweenthe proof-mass 102 and the electrodes. The mechanical and magneticstiffnesses are positive, while the electrostatic stiffness is negative.In an open loop configuration, the combined mechanical and magneticstiffness must be larger than the electrostatic stiffness to avoid anunstable configuration where the two capacitive plates snap down totheir mechanical limit. Closed loop feedback control allows the systemto operate in unstable regimes and achieve a higher scale factor withresulting performance benefits.

The mechanical stiffness (kmech) is fixed by the mechanical design ofthe support structure, and the magnetic stiffness is set by theproximity of the transducer 300 a or 300 b to the reference magnets 406and the resulting field magnitude. However, the voltage bias can betuned with high precision which gives the ability to arbitrarilygenerate a desired stiffness and corresponding scale factor. Low lossstructures common in vacuum packaged MEMS devices, can have adistinctive resonant frequency with a large response around its naturalfrequency where the input is also mechanically amplified. This frequencyregion, with high scale factor, can be arbitrarily tuned with themaximum frequency limited by the mechanical and magnetic stiffnessavailable. However, there is a tradeoff between scale factor andbandwidth where low stiffness structures mechanically filter frequenciesabout 2X above their resonant frequency.

According to certain embodiments, small, millimeter-scale proof-masses102 can be tuned over a frequency range of approximately 0 Hz (DC) to 1kHz while maintaining an acceptable scale factor and bias voltage. FIG.7 is a graph showing the simulated scale factor (SF) as a function offrequency for various bias voltages. Curve 502 corresponds to a biasvoltage of 35 volts (V); curve 504 corresponds to a bias voltage of 32V; and curve 506 corresponds to a bias voltage of 24 V. In this example,the magnetic field sensor 300 included an NdFeB magnet having dimensions5 mm by 5 mm by 2 mm, and the reference magnet field strength was 0.5 T.Higher bias voltages improve electronics noise and scale factor at lowfrequencies by reducing the total stiffness to near zero. Reducing thebias voltages sacrifices performance at low frequencies, but expands theoperational bandwidth of the device. In particular, at higherfrequencies, superior noise performance may be achieved by operatingaround the resonant peak and then applying a whitening filter tonormalize the amplitude and phase response output. It should be notedthat at the highest scale factors, the available travel in thecapacitive gap may cause the device to snap down if the background Earthfield is aligned with the input axis. This can be addressed by operatingwith closed loop feedback control to rebalance the sensor, or byoperating open loop with lower bias. Thus, the bias voltage and scalefactor, combined with other parameters of the gradiometer design,determine the noise floor. Contributors to noise include Brownian noise,noise from the pre-amplifier 314 and other electronics, external andself-generated magnetic noise, and hysteresis noise from the highpermeability shunt 408.

Brownian noise is the fundamental limit of the sensor regardless of theinstrument scale factor since the dynamics of the sensor respond to theresulting torque noise. Brownian noise generally describes the noisefloor of the device operating near its resonant peak. The magnitude ofthe thermo-mechanical agitation is dictated by losses in the system.Losses can be reduced by vacuum packaging the sensor, as discussedabove. Mechanical losses in the Silicon/MEMS structure, including thesupports, can be addressed by using a control loop with upper and lowersense plate electrodes to electrostatically levitate the magnet. In thiscase, losses may be limited by the magnet motion which induces eddycurrents in nearby conductors, or exercises the hysteresis loop ofnearby soft magnetic materials (such as the high permeability shunt408). Laminations and/or low conductive materials nearby (e.g. ceramicmagnets and packaging can be used to control these losses.

Voltage and current noise from the pre-amplifier 314 also limit thebroadband noise of the magnetic sensor 300, such that large pick-offcapacitors may be used. Movements of the proof-mass 102 may induce acurrent due to the variable capacitance with a bias applied across it.Performance may improve with higher scale factors and bias voltages. Incertain examples, stray capacitance can be minimized throughout thesignal chain. A carrier frequency (e.g. 10 kHz) and subsequentdemodulation back to baseband, as discussed above with reference to FIG.5 , may be used to avoid 1/f amplifier noise sources at low frequencies.Other components in the electronics and structure of the magnetic sensor300 can also produce noise in the measurements. For example, voltagenoise on any of the capacitive plates generates differential forces thatmove the proof-mass 102 and appear as a sensor input if they fall in thesense bandwidth. Filtering and noise control of the bias voltage canpartially help, but may not completely eliminate this noise source. Forexample, noise on any torque feedback plates is in-band by definition,and may be controlled by minimizing the voltage noise applied on thetorque plates. Increasing the capacitive gap extends the dynamic rangeand reduces the force, but also reduces scale factor which impactsbroadband noise performance. Johnson noise from conductors in thetransducers 300 a, 300 b or other components in the gradiometer 400 canalso impact performance. Conductors relatively close to the proof-masses102 may generate thermally induced eddy currents which produce magneticnoise. This may be generally avoided by using non-conductive (e.g.glass) packaging and structures in the vicinity of the proof-mass 102.However, it may be necessary for conductive surfaces, such as theelectrodes and other electrical traces, to be in close proximity to theproof-mass 102. For example, a 100 nm thick electrode plated to the topof the substrate 118 may generate more than 6 pT/√Hz of in-band noise atthe bottom of the MEMS structure 302 and 165 fT/√Hz when integratedthrough the volume. To address this noise source, in certain examples,the conductivity of the electrical traces may be reduced by about fourorders of magnitude and/or slots may be added to reduce enclosed eddycurrent paths. The resulting trace resistance remains less than the ~1kohm limit of the electronics, while reducing the integratedgradiometric noise to less than 0.25 fT/cm/√Hz.

As discussed above, operating the magnetic field sensors as agradiometer removes external magnetic noise (clutter) to the firstorder. However, the sensor electronics may generate large gradients thatmay need to be reduced or controlled. According to certain embodiments,the sensor electronics that are located in proximity to the proof-mass102 and MEMS structures may be placed in an internal shielded cavity, asdiscussed above, to reduce the effects of self-generated noise. Controlcircuitry of the gradiometer 400 external to the transducers 300 a, 300b may also be enclosed by magnetic shielding and connected by twistedpair wires to avoid generating interference at the transducers 300 a,300 b.

In certain implementations, hysteresis noise from the high permeabilityshunt 408 may induce noise into the transducers 300 a, 300 b. Forexample, this may be observed when the flux concentrators 134 areintegrated and placed close to the transducers. However, including theflux concentrators 134 may still be advantageous if the concentratorgeometry provides sufficient gain to compensate for the additionalnoise.

Analytical models for each of the non-system related noise sources weregenerated to estimate the performance of the gradiometer 400. Aseparation of 6.5 cm, with a maximum package area of 1 cm², was modeledto ensure that a gradiometer 400 with a compact design could operate ona wide range of platforms. FIGS. 8A and 8B are graphs showing simulationresults for a modeled example of the gradiometer 400. FIG. 8A is a graphof simulated magnetic gradient noise (fT/cm/√Hz) as a function offrequency (Hz). For the simulation that produced the results shown inFIG. 8A, the magnet (of the proof-mass 102) was modeled as an NdFeBmagnet having dimensions 5 mm by 3 mm by 0.4 mm, the reference magneticfield (B_(ref) from the reference magnets 406) was 0.5 T, f_(mech) = 400Hz, and the bias voltage was 26 V. In FIG. 8A, curve 508 represents thetotal RSS magnetic gradient noise, curve 510 represents the Browniannoise, curve 512 represents the pre-amplifier 314 voltage noise, curve514 represents the pre-amplifier 314 current noise, and curve 516represents the noise from the signal generator 310 force.

FIG. 8B shows simulation results for a configuration on the gradiometer400 where an electrostatic spring optimizes performance to achieve lowernoise by operating in narrowband mode at higher frequencies. FIG. 8B isa graph showing the total RSS magnetic gradient noise as a function offrequency (corresponding to curve 508 in FIG. 8A) for different biasvoltages. In FIG. 8B, curve 518 corresponds to a bias voltage of 35 V,curve 520- corresponds to a bias voltage of 33 V, and curve 522corresponds to a bias voltage of 24 V. As shown in FIG. 87B, thefrequency band, with low noise performance, can be chosen by selectingthe bias voltage. For the simulation results presented in FIG. 8B, thegradiometer 400 was modeled with an NdFeB magnet having dimensions 5 mmby 5 mm by 2 mm, B_(ref) = 0.5 T, and f_(mech) = 0 Hz.

Referring again to FIG. 6 , both magnetic sensors 300 a, 300 b maycommon mode (cancel) uniform temperature deviations, and thermalgradients may influence the thermal stability limit of the gradiometer400. The scale factor described in Equation (5) is driven bymagnetization magnitude of the permanent magnet material. As thetemperature approaches the Curie point of the material, thermalagitation introduces instabilities which cause the internal magneticdipoles to lose alignment and reduce the net magnetization, as shown inFIG. 9 . Around room temperature, typical hard magnets have asensitivity of approximately -0.1%/K. Thermal control, or compensatingto better than 1 mK, as may be desired for certain application, may bevery challenging. According to certain embodiments, stability may bemaintained without requiring precision thermal control or calibration byleveraging the fact that the magnetization impacts stability more thanthe DC scale factor. The magnetization directly influences the magneticspring stiffness which is a product of the remnant magnetization of thetransducers 300 a, 300 b and the restoring field provided by thereference magnets 406. This, in conjunction with the structuralstiffness, has a -10 PPM/K sensitivity due the sensitivity of theelastic modulus to temperature, directly impacts the resulting scalefactor. Advantageously, these factors also influence the resonantfrequency which can be easily monitored in a high-Q resonator. The scalefactor sensitivity can be controlled by adjusting the bias voltage tomaintain the resonant frequency at a chosen value. The scale factor cantherefore be stabilized to within the limits of the frequencymeasurement and control.

In various applications, including, for example, using aerialsurveillance from a mobile platform to identify submerged targets, itcan be highly advantageous to recover the full magnetic gradient tensor.For example, recovering the full magnetic gradient tensor may mitigatenoise associated with the environment (e.g. local geology noise) and thedynamics of the platform itself, and may also provide the capability todirectly solve for the source dipole magnitude, location, andorientation which provides orthogonal information to separate cluttersources from small target anomalies. These additional degrees of freedommay also be used in advanced clutter suppression algorithms. Inbiophysical applications, such a magneto-encephalography (MEG), thevector gradients may provide the ability to better localize correlateddipole layers in the cortex.

According to certain embodiments, the gradiometer 400 can be configuredinto a multi-element array to allow for recovery of the full gradienttensor. For complete definition of the full gradient tensor, there arenine gradient terms and three field magnitudes:

$\begin{bmatrix}\frac{\delta B_{x}}{\delta x} & \frac{\delta B_{x}}{\delta y} & \frac{\delta B_{x}}{\delta z} \\\frac{\delta B_{y}}{\delta x} & \frac{\delta B_{y}}{\delta y} & \frac{\delta B_{y}}{\delta z} \\\frac{\delta B_{z}}{\delta z} & \frac{\delta B_{z}}{\delta y} & \frac{\delta B_{z}}{\delta z}\end{bmatrix}^{- 1} \cdot \begin{pmatrix}B_{x} \\B_{y} \\B_{z}\end{pmatrix}$

However, there is redundancy in the matrix. Gauss’s Law and Ampere’s Lawcan be employed to show that the nine gradient terms only require fiveunique measurements to completely define the matrix since,

$\nabla \cdot \overset{\rightarrow}{B} = \frac{\delta B_{x}}{\delta x} + \frac{\delta B_{y}}{\delta y} + \frac{\delta B_{z}}{\delta z} = 0$

and,

$\nabla \times \overset{\rightarrow}{B} = \mu_{0} j + \mu_{0}\varepsilon_{0}\frac{\delta E}{\delta T} \approx 0 \approx \begin{bmatrix}\frac{\delta B_{z}}{\delta y} & - & \frac{\delta B_{y}}{\delta z} \\\frac{\delta B_{z}}{\delta x} & - & \frac{\delta B_{x}}{\delta z} \\\frac{\delta B_{y}}{\delta x} & - & \frac{\delta B_{x}}{\delta y}\end{bmatrix} \cdot$

FIG. 10 shows an example a two-element array 600 that be used for fullgradient tensor extraction. The two-element array 600 has the ability tomeasure all the components of the gradient matrix and vector field whichcompletely defines the magnetic potential. In the example shown in FIG.10 , the gradiometer array 600 includes two single-axis gradiometers 400a, 400 b, each of which corresponds to an embodiment of the gradiometer400 discussed above. The two gradiometers 400 a, 400 b are placed nextto one another, but oriented in opposite directions to exploit the shuntreturn path for the reference magnets 406 in each segment. Arrows 602,604, 606, and 608 illustrate the magnetization vectors. Themagnetization vectors are co-linear in the z direction, which preventsthe measurement of the magnetic field in this direction (Bz). However,as shown by arrows 606 and 608, the field lines bend around the cornerssuch that a transducer 300 c placed at the ends of the array 600 in theorthogonal direction to the other transducers 300 a, 300 b, will bemagnetized in the +/-x direction, enabling the measurement of Bz as wellas a redundant measurement of By. The six transducers 300 a, 300 b, 300c (labeled 1-6 in FIG. 10 ) can be connected and differenced such thatthe array 600 provides eleven independent gradient measurements(including six redundant measurements) and twelve field vectorsmeasurements (including redundant measurements). For example, the

$\frac{\delta B_{x}}{\delta x}$

gradient measurement can be obtained by differencing the measurementsfrom transducers 1 and 2 or 5 and 6; the

$\frac{\delta B_{z}}{\delta z}$

gradient measurement can be obtained by differencing the measurementsfrom transducers 3 and 4; the

$\frac{\delta B_{y}}{\delta x}$

gradient measurement can be obtained by differencing the measurementsfrom transducers 1 and 2 or 5 and 6; the

$\frac{\delta B_{y}}{\delta z}$

gradient measurement can be obtained by differencing the measurementsfrom transducers 1 and 6, 2 and 5, or and 3 and 4; and the

$\frac{\delta B_{x}}{\delta z}$

gradient measurement can be obtained by differencing the measurementsfrom transducers 1 and 6, 2 and 5, or 3 and 4. In certain examples themeasurement of the dx gradient may be slightly degraded by the smallerbaseline, which can be improved by increasing the separation betweeneach gradiometer 400 a, 400 b of the array 600.

According to certain embodiments, any number of gradiometers 400 can beintegrated to achieve multi-element arrays that can be used for avariety of applications. For example, larger two- or three-dimensionalarrays, with greater spatial coverage, can be combined in a 2Dcheckerboard pattern that leverages symmetries. Differences can then betaken between many different transducers on different gradiometerelements of the array to derive higher order spatial gradient terms.

As discussed above, examples of the magnetic gradiometers, gradiometersystems or arrays, and related methods described herein offer variousbenefits over typical magnetometers. For instance, examples describedherein can recover the full gradiometric tensor, which can be leveragedto reject clutter, identify a signal, and localize a source. A fulltensor solution provides a significant amount of additional informationrelative to scalar data alone, and eliminates ambiguities in knowledgeof the local field. In various examples, the electrostatic/magneticspring system described herein permits performance to be finely tunedwith the ability to trade bandwidth and noise. In various examples, themagnetic components stiffness correlates to scale factor. Accordingly,absolute measurement sensitivities and other effects can be removed bymonitoring the natural frequency of the resonant system and usingvoltage feedback in the tunable spring to maintain a constant scalefactor over other changes which influence stability and performance.

Various examples described herein are also less expensive thantraditional magnetometer systems and do not require precision optical orother expensive components to operate the system. In particularexamples, the described MEMS-based sensors are intrinsically small andlow-power. For example, an entire gradiometer system (including allsupport components) can be scaled from < 2 cm to larger volumes tooptimize performance to a desired noise floor.

Certain examples may also offer the benefit of integrated shielding. Forinstance, the magnetic gradiometer may have a cavity in an internalshunt that also doubles as a magnetic shield to minimize couplingbetween noise sources in the proximity to the electronics and thetransducers of the magnetic gradiometer. In some examples, the sensorscan be intentionally coupled via magnetic interactions with nearbysensors to enhance signal recovery and reduce the effective noise floor.The sensors can also provide the full vector magnetic field at highprecision and with low noise (-10 fT/√Hz) to aid in localization andother algorithms. The described designs can also be extended to othersensor modalities, such as an electric field, by replacing the magneticdipole with an electric dipole. The combined system can directly measurethe Poynting vector and deduce the direction to a source dipole.

According to certain embodiments, an electric field gradiometer isformed analogously to the magnetic sensor variant by replacing materialswith their electrical counterparts. For example, the magnetic dipoleformed from a permanent magnet is replaced with an electric dipole suchas an electret, while high permeability magnetic material is replacedwith a high dielectric constant or metallic material. Otherwise thefunctionality of the sensor and gradiometer are equivalent. Thus,referring again to FIG. 6 , an electric field gradiometer may be formedusing electric field sensors 200 instead of the magnetic field sensors300 a and 300 b, along with the other replacements discussed above.Similarly, an electric gradiometer array analogous to the magneticgradiometer array illustrated in FIG. 10 can be implemented as discussedabove. Combining arrays of magnetic and electric gradiometers providesthe ability to resolve the Poynting vector using all magnetic andelectric field components. Thus, an integrated electromagneticgradiometer array can be formed from integrating multiple magneticsensors 300, electric field sensors 200, and/or gradiometers 400.

Having described above several aspects of at least one example, it is tobe appreciated various alterations, modifications, and improvements willreadily occur to those skilled in the art. Such alterations,modifications, and improvements are intended to be part of thisdisclosure and are intended to be within the scope of the disclosure.Accordingly, the foregoing description and drawings are by way ofexample only, and the scope of the disclosure should be determined fromproper construction of the appended claims, and their equivalents.

What is claimed is: 1-20. (canceled)
 21. A magnetic gradiometer,comprising: a first torsionally operated microelectromechanical systems(MEMS) magnetic sensor having a capacitive read-out configured toprovide a first measurement of a received magnetic field; a secondtorsionally operated MEMS magnetic sensor coupled to the firsttorsionally operated MEMS magnetic sensor and having the capacitiveread-out configured to provide a second measurement of the receivedmagnetic field; and control electronics coupled to the first and secondtorsionally operated MEMS magnetic sensors and configured to determine amagnetic field gradient of the received magnetic field based the firstand second measurements from the first and second torsionally operatedMEMS electromagnetic sensors.
 22. The magnetic gradiometer of claim 21,wherein in each of the first and second torsionally operated MEMSmagnetic sensors includes: a proof-mass; a magnetic dipole sourcecoupled to the proof mass; a substrate having a substrate offset spacedefined therein, wherein the proof-mass is suspended above the substrateoffset space; and a first sense electrode disposed on the substratewithin the substrate offset space and positioned proximate theproof-mass, the first sense electrode being configured to measure achange in capacitance relative to the proof mass from torsional movementof the proof-mass in response to the received magnetic field at themagnetic dipole source.
 23. The magnetic gradiometer of claim 22,wherein each of the first and second torsionally operated MEMS magneticsensors further includes a counterbalance coupled to the proof-mass,wherein the magnetic dipole source is coupled to a first surface of theproof-mass and the counterbalance is coupled to a second surface of theproof-mass distal the magnetic dipole source.
 24. The magneticgradiometer of claim 22, wherein each of the first and secondtorsionally operated MEMS magnetic sensors further includes a secondsense electrode disposed on the substrate, and wherein the first senseelectrode and the second sense electrode are configured to provide adifferential capacitance measurement based on the change in capacitancefrom the torsional movement of the proof-mass.
 25. The magneticgradiometer of claim 22, wherein each of the first and secondtorsionally operated MEMS magnetic sensors further includes at least onedrive electrode positioned proximate the proof-mass and configured toproduce a feedback torque on the proof-mass.
 26. The magneticgradiometer of claim 22, wherein the magnetic dipole source is apermanent magnet.
 27. The magnetic gradiometer of claim 26, wherein thepermanent magnet is a Neodymium Iron Boron (NdFeB) rare Earth permanentmagnet.
 28. The magnetic gradiometer of claim 22, wherein each of thefirst and second torsionally operated MEMS magnetic sensors furtherincludes at least one support coupled to the proof-mass and configuredto suspend the proof-mass above the substrate offset space.
 29. Themagnetic gradiometer of claim 28, further comprising an electronicfeedback loop configured to stabilize a scale factor of the magneticgradiometer by monitoring and adjusting a resonant frequency of the atleast one support.
 30. The magnetic gradiometer of claim 23, furthercomprising a circuit board that electrically couples the firsttorsionally operated MEMS magnetic sensor to the second torsionallyoperated MEMS magnetic sensor, wherein the control electronics is formedon the circuitboard.
 31. The magnetic gradiometer of claim 30, furthercomprising a reference structure that magnetically couples the firsttorsionally operated MEMS magnetic sensor to the second torsionallyoperated MEMS magnetic sensor.
 32. The magnetic gradiometer of claim 31,further comprising at least one reference magnet that produces areference magnetic field configured to mutually align the first andsecond torsionally operated MEMS magnetic sensors to a common vectorsuch that their magnetic moments are aligned.
 33. The magneticgradiometer of claim 32, further comprising a high permeability shuntthat couples together the first and second torsionally operated MEMSmagnetic sensors and the at least one reference magnet.
 34. The magneticgradiometer of claim 33, wherein the high permeability shunt includes asoft ferrite cage configured to provide shielding for the controlelectronics.
 35. An electric field gradiometer, comprising: a firsttorsionally operated microelectromechanical systems (MEMS) electricfield sensor having a capacitive read-out configured to provide a firstmeasurement of a received electric field; a second torsionally operatedMEMS electric field sensor coupled to the first torsionally operatedMEMS electric field sensor and having the capacitive read-out configuredto provide a second measurement of the received electric field; andcontrol electronics coupled to the first and second torsionally operatedMEMS electric field sensors and configured to determine an electricfield gradient of the received electric field based the first and secondmeasurements from the first and second torsionally operated MEMSelectric field sensors.
 36. The electric field gradiometer of claim 35,further comprising at least one electric field generator that produces areference field configured to mutually align the first and secondtorsionally operated MEMS electric field sensors to a common vector suchthat their electric dipole moments are aligned.
 37. A gradiometer systemcomprising: at least two magnetic gradiometers, each magneticgradiometer including: a first torsionally operatedmicroelectromechanical systems (MEMS) magnetic sensor having a firstmagnetic field capacitive read-out configured to provide a firstmeasurement of received magnetic field, a second torsionally operatedMEMS magnetic sensor coupled to the first torsionally operated MEMSmagnetic sensor and having a second magnetic field capacity read-outconfigured to provide a second measurement of the received magneticfield, and magnetic sensor control electronics coupled to the first andsecond torsionally operated MEMS magnetic sensors and configured todetermine a magnetic field gradient of the received magnetic field basedon the first and second measurements from the first and secondtorsionally operated MEMS electromagnetic sensors.
 38. The gradiometersystem of claim 37, further comprising at least one electric fieldgenerator that produces a reference field configured to mutually alignthe first and second torsionally operated MEMS electric field sensors toa common vector such that their electric dipole moments are aligned. 39.The gradiometer system of claim 38, wherein each of the first and secondtorsionally operated MEMS magnetic sensor includes: a proof-mass; amagnetic dipole source coupled to the proof mass; a substrate having asubstrate offset space defined therein, wherein the proof-mass issuspended above the substrate offset space; and a first sense electrodedisposed on the substrate within the substrate offset space andpositioned proximate the proof-mass, the first sense electrode beingconfigured to measure a change in capacitance relative to the proof massfrom torsional movement of the proof-mass in response to the receivedmagnetic field at the magnetic dipole source.
 40. The magneticgradiometer of claim 19, wherein each of the first and secondtorsionally operated MEMS magnetic sensors further includes acounterbalance coupled to the proof-mass, wherein the magnetic dipolesource is coupled to a first surface of the proof-mass and thecounterbalance is coupled to a second surface of the proof-mass distalthe magnetic dipole source.